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Theorems · Theorem · group theory

MulHom.domRestrict_apply

∀ {M : Type u_1} {σ : Type u_4} [inst : Mul M] {N : Type u_5} [inst_1 : Mul N] [inst_2 : SetLike σ M]
  [inst_3 : MulMemClass σ M] (f : M →ₙ* N) {S : σ} (x : ↥S), (f.domRestrict S) x = f ↑x
Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
Cited by
1 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
MulMulSetLikeMulMemClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MulHom.restrict_apply · cited by 0MulHom.restrict_applyDFunLike.coe · cited by 62936DFunLike.coeSetLike · cited by 1084SetLikeMulHom · cited by 299MulHomMulMemClass · cited by 25MulMemClassMulHom.domRestrict · cited by 2MulHom.domRestrictMulHom.domRestrict_applyCITED BYCITES

Cites5

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Cited by1

Results whose statement or proof uses this declaration.